Related papers: Matrix product state renormalization
The amplitude encoding of an arbitrary $n$-qubit state vector requires $\Omega(2^n)$ gate operations, owing to the exponential dimension of the Hilbert space. We can, however, form dimensionality-reduced representations of quantum states…
Ground-state preparation is a fundamental task in quantum simulation, because the overlap of the prepared state with the true ground state significantly affects the overall cost of subsequent quantum algorithms. We propose a three-stage…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
Efficient encoding of classical information plays a fundamental role in numerous practical quantum algorithms. However, the preparation of an arbitrary amplitude-encoded state has been proven to be time-consuming, and its deployment on…
It is well known that the matrix product state (MPS) description of a gapped ground state with a global on-site symmetry can exhibit "symmetry fractionalization". Namely, even though the symmetry acts as a linear representation on the…
The density matrix renormalization group (DMRG) has been extended to study quantum phase transitions on random graphs of fixed connectivity. As a relevant example, we have analysed the random Ising model in a transverse field. If the…
In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that…
Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…
In approximate ground states obtained from imaginary-time evolution, the spectrum of the state -- its decomposition into exact energy eigenstates -- falls off exponentially with the energy. Here we consider the energy spectra of approximate…
We consider the simplest inhomogeneous Matrix-Product-State for an open chain of N quantum spins that involves only two angles per site and two angles per bond with the following direct physical meanings. The two angles associated to the…
We present a new wavefunction ansatz that combines the strengths of spin projection with the language of matrix product states (MPS) and matrix product operators (MPO) as used in the density matrix renormalization group (DMRG).…
The matrix product state (MPS) belongs to the most important mathematical models in, for example, condensed matter physics and quantum information sciences. However, to realize an $N$-qubit MPS with large $N$ and large entanglement on a…
We use the finite-entanglement scaling of infinite matrix product states (iMPS) to explore supposedly infinite order transitions. This universal method may have lower computational costs than finite-size scaling. To this end, we study…
Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently,…
We consider integrable Matrix Product States (MPS) in integrable spin chains and show that they correspond to "operator valued" solutions of the so-called twisted Boundary Yang-Baxter (or reflection) equation. We argue that the…
We consider the preparation of matrix product states (MPS) on quantum devices via quantum circuits of local gates. We first prove that faithfully preparing translation-invariant normal MPS of $N$ sites requires a circuit depth…
Using truncated conformal field theory (CFT), we present the formalism necessary to obtain exact matrix product state (MPS) representations for any fractional quantum hall model state which can be written as an expectation value of primary…
We study the set of random matrix product states (RMPS) introduced in arXiv:0908.3877 as a tool to explore foundational aspects of quantum statistical mechanics. In the present work, we provide an accurate numerical and analytical…
This work presents a method for studying low-energy physics in highly correlated magnetic systems using the matrix product state (MPS) manifold. We adapt the spin-wave approach, which has been very successful in modeling certain…
Matrix-product states and their continuous analogues are variational classes of states that capture quantum many-body systems or quantum fields with low entanglement; they are at the basis of the density-matrix renormalization group method…